The conventional ₁₄C method relies on the accurate measurement of a beta-ray decay rate to determine the age of the sample. The new method instead uses an ultrasensitive mass spectrometer to count the individual ₁₄C atoms in a sample. The problem of cosmic ray background does not arise. Shorter counting times on samples 1,000 times smaller will be possible. One result will be production of more accurate age determinations. The new method will permit a great expansion in the types of archaeological materials that can be dated because only milligram samples will be required. Research on the design of a dedicated ₁₄C atom counting machine is presently in progress.